NCERT Solutions for class 8 Maths chapter 4 Practical geometry exercise 4.1

Exercise 4.1

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Introduction - "Practical Geometry" Chapter 4 - NCERT Class 8th Maths Solutions

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Q 1 - Ex 4.1 - Practical Geometry - NCERT Maths Class 8th - Chapter 4

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Question 1
Construct the following quadrilaterals.
(i) Quadrilateral ABCD
AB = 4.5 cm
BC = 5.5 cm
CD = 4 cm
AD = 6 cm
AC = 7 cm
Sol :
Firstly, a rough sketch of this quadrilateral can be drawn as follows.

(Step-1) ΔABC can be constructed by using the given measurements as follows.

(Step-2) Vertex D is 6 cm away from vertex A. Therefore, while taking A as centre, draw an arc of radius 6 cm.

(Step-3) Taking C as centre, draw an arc of radius 4 cm, cutting the previous arc at point D. Join D to A and C.

ABCD is the required quadrilateral.

(ii) Quadrilateral JUMP
JU = 3.5 cm
UM = 4 cm
MP = 5 cm
PJ = 4.5 cm
PU = 6.5 cm
Sol :
Firstly, a rough sketch of this quadrilateral can be drawn as follows.

(Step-1) Δ JUP can be constructed by using the given measurements as follows.

(Step-2) Vertex M is 5 cm away from vertex P and 4 cm away from vertex U. Taking P and U as centres, draw arcs of radii 5 cm and 4 cm respectively. Let the point of intersection be M.

(Step-3) Join M to P and U.

JUMP is the required quadrilateral.


(iii) Parallelogram MORE
OR = 6 cm
RE = 4.5 cm
EO = 7.5 cm
Sol :
We know that opposite sides of a parallelogram are equal in length and also these are parallel to each other.
Hence, ME = OR, MO = ER
A rough sketch of this parallelogram can be drawn as follows.

(Step-1) Δ EOR can be constructed by using the given measurements as follows.

(Step-2) Vertex M is 4.5 cm away from vertex O and 6 cm away from vertex E. Therefore, while taking O and E as centres, draw arcs of 4.5 cm radius and 6 cm radius respectively. These will intersect each other at point M.

(Step-3) Join M to O and E.

MORE is the required parallelogram.

(iv) Rhombus BEST
BE = 4.5 cm
ET = 6 cm
Sol :
We know that all sides of a rhombus are of the same measure.
Hence, BE = ES = ST = TB
A rough sketch of this rhombus can be drawn as follows.

(Step-1) Δ BET can be constructed by using the given measurements as follows.

(Step-2) Vertex S is 4.5 cm away from vertex E and also from vertex T. Therefore, while taking E and T as centres, draw arcs of 4.5 cm radius, which will be intersecting each other at point S.

(Step-3) Join S to E and T.

BEST is the required rhombus.